Probabilistic latent variable regression model for process-quality monitoring

Online monitoring of chemical industrial processes is crucial to the healthy assessment of the operation status. In recent years, the monitoring schemes based on probabilistic principal component analysis (PPCA) models have been developed and applied in industries. PPCA is an effective tool for detecting the variations of process variables but does not utilize quality variables. In this paper, the probabilistic latent variables regression (PLVR) is proposed. It extends the monitoring framework of PPCA by including the quality information for monitoring performance improvement. The PLVR model calibrated by the expectation-maximization algorithm is systematically developed. In PLVR, the effective latent variables, which are more sensitive to the variations of quality variables by monitoring the input subspace, can be determined through the covariance with information from the process and the quality variables. With this novel PLVR model, new statistics for PLVR is also presented for easy tracking of the operating process. It can also monitor the occurrence of the upsets of product qualities. Finally, the advantages of the proposed method over PPCA are presented through a case study of the Tennessee Eastman benchmark process characterized by fault sources.